34 Mr Basset, On the Stability of [Nov. 28, 



Accordingly 



+ i o2 (-T{A,rf l~,P.'l"jjP'f <il^ -(19). 

 where in the last term m has any of the values 1, 2, 3 ... n. 



From the ordinary formulae for relative equilibrium 



pg = (A-a>^)c\l+y'), pg = Gcy, 



from the last of which we obtain 



pg = ^7rpc'ry(l+y')p^q^ (20); 



whilst the elimination of pg gives the ordinary equation for &)^ 

 We thus obtain 



jJ9-'dS = ^P.q.jJl^ (-r^r ^i i^r (f^) COS m^rj d^dir 



(21). 



To calculate the last term of (15) we have 



I-I^ = p (r, + l\yd\dS 



= pjjr,'ad8 + pjjryidS. 



Since the square of this quantity occurs, we may neglect the 

 last term in the integral, whence 



^ -^0 = ^ (1 + 7^) //(I - f^')t{-r'^,A-P:\,.)cosmfd,.dir 



= I PO' (1 + 7^)/£ a - f^') 2^„P„ (H')dfi. 



Since the mass of the new figure is equal to that of the old, 

 JadS = 0; whence ^^^^O; also since 



we finally obtain 



I-Io = ^po\l + y')A^ (22). 



